ON CONFORMALLY BERWALD M-TH ROOT (α, β)-METRICS

Abstract

In this paper, we study the class of $m$-th root (α, β)-metrics which is a significant class mixed of two classes of metrics: $m$-th root metrics and (α, β)-metrics. First, we find the necessary and sufficient condition under which the quartic (α, β)-metrics are conformally Berwald. Then, we find the necessary and sufficient condition under which the cubic (α, β)-metrics are conformally Berwald. Finally, we construct some conformal Finslerian invariants.